Biomedical subjects

David Holcman

Publications and source records attributed to David Holcman.

6 recordsLinked to original sources

PubMed2006

Modeling synaptic dynamics driven by receptor lateral diffusion.

The synaptic weight between a pre- and a postsynaptic neuron depends in part on the number of postsynaptic receptors. On the surface of neurons, receptors traffic by random motion in and out from a microstructure called the postsynaptic density (PSD). In the PSD, receptors can be stabilized at the membrane when they bind to scaffolding proteins. We propose a mathematical model to compute the postsynaptic counterpart of the synaptic weight based on receptor trafficking. We take into account the receptor fluxes at the PSD, which can be regulated by neuronal activity, and the interactions of receptors with the scaffolding molecules. Using a Markovian approach, we estimate the mean and the fluctuations of the number of bound receptors. When the number of receptors is large, a deterministic system is also derived. Moreover, these equations can be used, for example, to fit fluorescence-recovery-after-photobleaching experiments to determine, in living neurons, the chemical binding constants for the receptors/scaffolding molecules interaction at synapses.

Algorithms↗

PubMed2006

The emergence of Up and Down states in cortical networks.

The cerebral cortex is continuously active in the absence of external stimuli. An example of this spontaneous activity is the voltage transition between an Up and a Down state, observed simultaneously at individual neurons. Since this phenomenon could be of critical importance for working memory and attention, its explanation could reveal some fundamental properties of cortical organization. To identify a possible scenario for the dynamics of Up-Down states, we analyze a reduced stochastic dynamical system that models an interconnected network of excitatory neurons with activity-dependent synaptic depression. The model reveals that when the total synaptic connection strength exceeds a certain threshold, the phase space of the dynamical system contains two attractors, interpreted as Up and Down states. In that case, synaptic noise causes transitions between the states. Moreover, an external stimulation producing a depolarization increases the time spent in the Up state, as observed experimentally. We therefore propose that the existence of Up-Down states is a fundamental and inherent property of a noisy neural ensemble with sufficiently strong synaptic connections.

Action Potentials↗

PubMed2005

Survival probability of diffusion with trapping in cellular neurobiology.

The problem of diffusion with absorption and trapping sites arises in the theory of molecular signaling inside and on the membranes of biological cells. In particular, this problem arises in the case of spine-dendrite communication, where the number of calcium ions, modeled as random particles, is regulated across the spine microstructure by pumps, which play the role of killing sites, while the end of the dendritic shaft is an absorbing boundary. We develop a general mathematical framework for diffusion in the presence of absorption and killing sites and apply it to the computation of the time-dependent survival probability of ions. We also compute the ratio of the number of absorbed particles at a specific location to the number of killed particles. We show that the ratio depends on the distribution of killing sites. The biological consequence is that the position of the pumps regulates the fraction of calcium ions that reach the dendrite.

Animals↗

PubMed2005

The limit of photoreceptor sensitivity: molecular mechanisms of dark noise in retinal cones.

Detection threshold in cone photoreceptors requires the simultaneous absorption of several photons because single photon photocurrent is small in amplitude and does not exceed intrinsic fluctuations in the outer segment dark current (dark noise). To understand the mechanisms that limit light sensitivity, we characterized the molecular origin of dark noise in intact, isolated bass single cones. Dark noise is caused by continuous fluctuations in the cytoplasmic concentrations of both cGMP and Ca(2+) that arise from the activity in darkness of both guanylate cyclase (GC), the enzyme that synthesizes cGMP, and phosphodiesterase (PDE), the enzyme that hydrolyzes it. In cones loaded with high concentration Ca(2+) buffering agents, we demonstrate that variation in cGMP levels arise from fluctuations in the mean PDE enzymatic activity. The rates of PDE activation and inactivation determine the quantitative characteristics of the dark noise power density spectrum. We developed a mathematical model based on the dynamics of PDE activity that accurately predicts this power spectrum. Analysis of the experimental data with the theoretical model allows us to determine the rates of PDE activation and deactivation in the intact photoreceptor. In fish cones, the mean lifetime of active PDE at room temperature is approximately 55 ms. In nonmammalian rods, in contrast, active PDE lifetime is approximately 555 ms. This remarkable difference helps explain why cones are noisier than rods and why cone photocurrents are smaller in peak amplitude and faster in time course than those in rods. Both these features make cones less light sensitive than rods.

Adaptation, Ocular↗

PubMed2004

Longitudinal diffusion in retinal rod and cone outer segment cytoplasm: the consequence of cell structure.

Excitation signals spread along photoreceptor outer segments away from the site of photon capture because of longitudinal diffusion of cGMP, a cytoplasmic second messenger. The quantitative features of longitudinal diffusion reflect the anatomical structure of the outer segment, known to be profoundly different in rod and cone photoreceptors. To explore how structural differences affect cytoplasmic diffusion and to assess whether longitudinal diffusion may contribute to the difference in signal transduction between photoreceptor types, we investigated, both theoretically and experimentally, the longitudinal diffusion of small, hydrophilic molecules in outer segments. We developed a new theoretical analysis to explicitly compute the longitudinal diffusion constant, Dl, in terms of outer segment structure. Using time-resolved fluorescence imaging we measured Dl of Alexa488 and lucifer yellow in intact, single cones and validated the theoretical analysis. We used numerical simulations of the theoretical model to investigate cGMP diffusion in outer segments of various species. At a given time interval, cGMP spreads further in rod than in cone outer segments of the same dimensions. Across all species, the spatial spread of cGMP at the peak of the dim light photocurrent is 3-5 microm in rod outer segments, regardless of their absolute size. Similarly the cGMP spatial spread is 0.7-1 microm in cone outer segments, independently of their dimensions.

Animals↗

PubMed2004

Dynamic regulation of spine-dendrite coupling in cultured hippocampal neurons.

We investigated the role of dendritic spine morphology in spine-dendrite calcium communication using novel experimental and theoretical approaches. A transient rise in [Ca2+]i was produced in individual spine heads of Fluo-4-loaded cultured hippocampal neurons by flash photolysis of caged calcium. Following flash photolysis in the spine head, a delayed [Ca2+]i transient was detected in the parent dendrites of only short, but not long, spines. Delayed elevated fluorescence in the dendrite of the short spines was also seen with a membrane-bound fluorophore and fluorescence recovery from bleaching of a calcium-bound fluorophore had a much slower kinetics, indicating that the dendritic fluorescence change reflects a genuine diffusion of free [Ca2+]i from the spine head to the parent dendrite. Calcium diffusion between spine head and the parent dendrite was regulated by calcium stores as well as by a Na-Ca exchanger. Spine length varied with the recent history of the [Ca2+]i variations in the spine, such that small numbers of calcium transients resulted in elongation of spines whereas large numbers of calcium transients caused shrinkage of the spines. Consequently, spine elongation resulted in a complete isolation of the spine from the dendrite, while shrinkage caused an enhanced coupling with the parent dendrite. These studies highlight a dynamically regulated coupling between a dendritic spine head and its parent dendrite.

Animals↗